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A Meshless Method for the Numerical Solution of the 2-and 3-D Semiconductor Poisson Equation

Summary: A Meshless Method for the Numerical Solution of the 2- and 3-D Semiconductor
Poisson Equation
C.J. Wordelman, N.R. Aluru, U. Ravaioli1
Abstract: This paper describes the application of the mesh-
less Finite Point (FP) method to the solution of the nonlin-
ear semiconductor Poisson equation. The FP method is a
true meshless method which uses a weighted least-squares fit
and point collocation. The nonlinearity of the semiconduc-
tor Poisson equation is treated by Newton-Raphson iteration,
and sparse matrices are employed to store the shape function
and coefficient matrices. Using examples in two- and three-
dimensions (2- and 3-D) for a prototypical n-channel MOS-
FET, the FP method demonstrates promise both as a means of
mesh enhancement and for treating problems where arbitrary
point placement is advantageous, such as for the simulation of
carrier wave packet and dopant cloud effects in the ensemble
Monte Carlo method. The validity of the solutions and the ca-
pability of the method to treat arbitrary boundary conditions is
shown by comparison with finite difference results.
keyword: finite point methods, meshless methods, mesh


Source: Aluru, Narayana R. - Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign


Collections: Engineering; Materials Science